Eight women who are suing Scotland Yard over the conduct of undercover officers who had sexual relationships with them have refused to cooperate with a police investigation.

In what their lawyer said was a blow to the investigation's credibility, the women – who are key witnesses – said in a letter that they would no longer be involved owing to the police's "neither confirm, nor deny policy, which could prevent them from ever learning the details about the abuse they claim to have suffered".

The letter to Mick Creedon, the chief constable who is leading Operation Herne, comes after Doreen Lawrence demanded a public inquiry into allegations that Metropolitan police officers attempted to smear her after her son's murder.

"They are pretty key witnesses because they can talk a lot about one of the key areas of the investigation," said Harriet Wistrich, the women's solicitor.

She added that there were now few circumstances under which her clients would be willing to cooperate because of a loss of trust. Officers working on the investigation have, she said, told her that it is policy to neither confirm nor deny any details related to the work of undercover officers in order to protect former, serving and future officers. But, she added, police have confirmed details in the past.

"They want this to be investigated, the problem is that what they are being offered gives them no guarantee of finding out anything," said Wistrich. Her letter follows requests from undercover police officer turned whistleblower Peter Francis to be exempt from prosecution under the Official Secrets Act before he decided whether or not to give evidence.

Lawrence's lawyer, Imran Khan, demanded that the investigation go even further, saying that Francis "should be giving evidence to a public inquiry, not staying behind closed doors and speaking to police officers. That's the whole point of calling for an inquiry".

Legal action began in December 2011 against the Metropolitan police on behalf of the eight women who claim they were deceived into having long-term intimate relationships with undercover police officers.

It is claimed five undercover officers engaged in infiltrating environmental campaign groups between the mid 1980s and 2010 had relationships with the women lasting from seven months to nine years.

Bob Lambert, John Dines, Jim Boyling, Mark Cassidy and Mark Kennedy have been named as the alleged undercover officers. The women will now only cooperate with an independent investigation or public inquiry, the solicitors said.

The firm claims the Metropolitan police have threatened to apply to have the women's allegations struck out as unfair to the police and to apply for a "closed material procedure" hearing under the powers of the new Justice and Security Act.

This means the police can keep evidence secret - they could put material before the judge which neither the claimants nor their lawyers would be able to see or challenge.

The group of women claim the undercover officers' actions breached their human rights as protected by the European Convention on Human Rights, including Article 3, which prohibits inhumane and degrading treatment, and Article 8, which protects private and family life.

They are also bringing claims for deceit, assault, misfeasance in public office and negligence.

Herne was set up in October 2011 to look into allegations made against the Met's Special Demonstration Squad (SDS), including using dead children's identities and engaging in inappropriate sexual relationships.

A raft of allegations have been made since former Pc Mark Kennedy was unmasked in 2011 as an undercover officer who spied on environmental protesters as long-haired dropout Mark "Flash" Stone.A Met spokesman said: "There is a thorough review and live investigation into allegations of inappropriate behaviour and practices involving historic undercover deployments. It would be inappropriate for us to provide a running commentary on specific allegations whilst this investigation is ongoing."